Windows 7 (as well as Vista) pretty much requires you to run the games as an 'admin'. To do that, right-click the executable file and choose Properties. Click the Advanced button and check the box marked "Run as Administrator" and OK your way back out. Do this for all three versions.
You should really enter your serial numbers into your Profile because this is the only way you will have access to the Download Station and the only way anyone on this forum knows you have properly registered copies of the games.
My solution may not help you with your problem though; so post back if you are still having difficulties.
It also wouldn't hurt to list your system specifications (CPU, RAM, Video card, and the like).
EDIT: To register your serial numbers, click on the Profile link at the top of the page and go to Trainz -> Serial Number and enter the codes for each game.
Bill